Settling into dry granular media in different gravities

Abstract

Key Points:• The settling depth in granular media is independent of gravity • The settling time scales like g −1∕2• Layering driven by granular sedimentation should be similar Abstract While the penetration of objects into granular media is well-studied, there is little understanding of how objects settle in gravities, g eff , different from that of Earth-a scenario potentially relevant to the geomorphology of planets and asteroids and also to their exploration using man-made devices. By conducting experiments in an accelerating frame, we explore g eff ranging from 0.4 g to 1.2 g. Surprisingly, we find that the rest depth is independent of g eff and also that the time required for the object to come to rest scales like g. With discrete element modeling simulations, we reproduce the experimental results and extend the range of g eff to objects as small as asteroids and as large as Jupiter. Our results shed light on the initial stage of sedimentation into dry granular media across a range of celestial bodies and also have implications for the design of man-made, extraterrestrial vehicles and structures.A loosely packed bed of sand sits precariously on the fence between mechanically stable and flowing states. This has especially strong implications not only for the geomorphology of the Earth but for that of extraterrestrial bodies where the surface is predominantly granular [Shinbrot et al., 2004;Almeida et al., 2008;Thomas and Robinson, 2005;Asphaug, 2007;Miyamoto et al., 2007]. Beyond surface morphology, extraterrestrial exploration and development requires navigation in and on loose granular media, but little is known regarding how objects settle in granular systems with gravitational conditions different from Earth's. Such understanding may have helped prevent the difficulties encountered by the Mars rover, Spirit, as it sank into and tried to escape from a sand dune in 2009 (see, for example, http://marsrover.nasa.gov/spotlight/ 20091019a.html). Other endeavors, such as asteroid or lunar mining [Elvis, 2012], will certainly involve both navigation and construction on granular surfaces.During the last decade, our understanding of the resistance to objects penetrating into granular media under Earth-like conditions has advanced quickly [Uehara et al., 2003;Walsh et al., 2003;Boudet et al., 2006;de Vet and de Bruyn, 2007;Katsuragi and Durian, 2007;Pacheco-Vázquez et al., 2011;Katsuragi, 2012;Kondic et al., 2012;Ruiz-Suárez, 2013]. A handful of attempts have mimicked low-gravity conditions [Goldman and Umbanhowar, 2008;Brzinski and Durian, 2010;Chen et al., 2009;Constantino et al., 2011;Dorbolo et al., 2013;Brzinski et al., 2013], mainly by using air-fluidized granular beds or grains immersed in a liquid, but the main focus has typically been on the role of intruder velocity or grain friction. Here we focus exclusively on the role of gravity as an object settles into granular media. By conducting experiments in a freely falling reference frame, we are able to create true low-and high-gravity conditions as a sphere...

Collisional model of energy dissipation in three-dimensional granular impact

“…However,z(t) has more amplified noise in part due to repeated differentiation and convolution which can distort the curves. It is therefore difficult to resolve force fluctuations from the granular medium, which have been observed in other experiments as an indication of the building and breaking up of force chains [12,21,26]. We comparez(t) determined from highspeed imaging to that of direct force measurements via an accelerometer (Analog Devices ADXL377, sample rate = 500 Hz), where the imaging and accelerometer measurements are taken simultaneously (see fig.…”

“…There has been significant effort to understand the way by which momentum is transferred to granular media, beginning over a century ago [1]. Studies of penetration into dry granular media have expanded significantly to focus on crater formation [2][3][4][5][6][7][8] and proposed governing force laws [9][10][11][12][13]. Additionally, a complete comprehension of granular impact has a natural connection to navigation on grainy surfaces [14,15], geomorphology, and astrophysical craters [16][17][18][19].…”

Depth-Dependent Resistance of Granular Media to Vertical Penetration

“…First, while the total stopping force points up, the extent to which friction acts locally normal versus tangential to surface area elements of the projectile is not known. Second, while FðzÞ has been shown to grow with gravitational loading of the bed [22,23], it is unknown how the motion loading of contacts by the intruder affects the total stopping force. In particular, force chains extend from the projectile deep into the medium and are intermittently loaded and broken during impact [17,[24][25][26]; this could contribute to friction.…”

“…gð1 À U=U c Þ, where U c is the fluidization airspeed where the upflow exactly balances gravity. Thus, without actually changing gravitational acceleration [10,22,23], the effective gravity loading is reduced by a subfluidizing upflow, 0 < U < U c , similarly, it is enhanced by a downflow, U < 0. The motion loading of contacts, and the inertial drag force, ought not be affected by airflow.…”

Note: “Lock-in accelerometry” to follow sink dynamics in shaken granular matter

“…But video techniques are of no use to study the penetration into a 3D system of nontransparent grains, where the dynamics can be quite complex 9 . In those cases, wireless accelerometry constitutes a natural alternative that has been used in very few occasions, as far as we know [10][11][12][13] .…”